My vehicle says Premium is recommended.
Your take...?
Do what your automobile manufacturer recommends. They aren't getting any cut of the gasoline money after the sale.
Why?
Your particular car is tuned to work best with premium gasoline. For non-turbo'ed cars, the engine is expecting to get higher octane gasoline so that it will burn more consistently for every 3rd cycle (the first cycle is insertion of air/gas mixture, the second cycle is compression, and the third cycle is combustion of the air/gas mixture). The fourth cycle pushes out the exhaust gases, which contains unburnt gasoline.
You might ask, what's the big deal? So I get a little less HP per cycle.
When you go to a gas station who 'illegally' dilutes their gasoline with water, that will decrease the octane. When you put this into your car, and your car doesn't need premium gas i.e. 87 octane for your car, you'll get what is called knocking or pinging. When you put in non-premium gas into a car that needs premium gas, you are doing the same thing.
The problem is that cheaper gasoline allows for more unburnt gasoline in the cylinders which can detonate or burn at the wrong time of the cycle. This creates a knock in your engine. These knocks will harm your engine.
For turbo'ed cars, your car will spray in more fuel into the air/fuel mixture for the higher fuel needs. When you are using 87 octane, you are exacerbating the situation. Turbos push more air and fuel into the cylinder and it aids in compression (superchargers do the same thing). This results in a stronger third cycle explosion. To note, a turbo'ed 2 liter, 4 cylinder engine has the same volume of air in each cylinder chamber as a non-turboed 2 liter, 4 cylinder engine. Turbo-charged engines usually require you to retard their timing, i.e. the spark goes off a little later in their third stroke/cycle rather than at TDC (top dead center) for that cylinder. If it's too early, it will result in knock. I'm not super good at explaining why, but that's the case. If you've put in cheap gas, and the timing is retarded, and even more gasoline is unburnt within the cylinder after BDC (bottom dead center). Your knock or ping is going to be even greater and will damage your engine even more.
Why does non-turbo'ed BMW need premium gas and a Toyota Corolla can do with non-premium gas?
The internal combustion engine is very inefficient. Think about a top fuel drag race car. All the flames coming out of the headers is unspent gasoline. This happens on a much smaller scale in a regular car. Your intake valves take in the air/fuel mix on the first stroke. The intake valves close on the second stroke. The exhaust valves open on the fourth stroke and close on the first stroke. On paper, that's the most efficient. But in reality, The intake valve stays a bit open at the beginning of the second stroke and the exhaust valves start opening on their third stroke before it hits top dead center. What BMW does it try to make the engine more efficient. They try to keep the exhaust valves from opening as early so more torque can be extracted per every third stroke. They try to close the intake valves sooner in the beginning of the second stroke. Putting in stronger valve springs is part of the solution. Modifying the cams is also done. In order to get the engine to work with these these modified intake/exhaust times AND to avoid pinging, they require you to put in premium gas.